Spatial radiation modulator pattern generation
A method of generating a design pattern for a spatial radiation modulator to encode two or more selected spectral components in one or more spectral ranges for the chemometric analysis of a group of analytes. The method includes obtaining a corresponding spectrum for each of the analytes, defining a set of initial spectral windows, constructing a chemometric matrix to relate concentrations of the analytes to intensities of the spectral components, deriving optimized spectral windows, and translating the center wavelength and the bandwidth of each of the optimized spectral windows into a corresponding optimized annular region on the modulator.
1. A method for generating a design pattern for a spatial radiation modulator to encode two or more selected spectral components in one or more spectral ranges for the chemometric analysis of a group of analytes, said modulator employed in an optical system comprising at least one radiation source and dispersive optics to produce at least one dispersed image along at least one radial axis of said modulator substantially according to a dispersion function, said dispersion function relating radial positions on said modulator to dispersed spectral components in the at least one dispersed image; said method comprising:
obtaining a corresponding spectrum for each of said analytes in said group, each said spectrum having at least one spectral feature in at least one of said spectral ranges;
defining a set of at least two initial spectral windows, each said spectral window comprising a center wavelength and a bandwidth, each of said initial spectral windows falling within at least one of said spectral ranges, said spectral windows corresponding to said selected spectral components;
constructing a chemometric matrix to relate concentrations of said analytes in said group to intensities of said spectral components;
deriving from said chemometric matrix optimized spectral windows; and
translating said center wavelength and said bandwidth of each of said optimized spectral windows into a corresponding optimized annular region on said modulator, said annular region comprising a corresponding optimized radial position and optimized radial width.
2. The method of claim 1 , further comprising forming on a substrate a plurality of sub-regions having optical characteristics substantially different from said substrate so that said sub-regions comprises substantially said pattern, and patterning said sub-regions within said annular region or segment of said annular region so that said sub-regions modulate the intensity of radiation from the source according to a modulation function.
3. The method of claim 1 , wherein said deriving comprises:
calculating a noise merit function of said chemometric matrix, wherein said merit function gauges concentration error of each of said analytes as a function of intensity uncertainty of said spectral components; and
optimizing said chemometric matrix, wherein said optimizing includes varying the center wavelength and bandwidth of said initial spectral windows to define said optimized spectral windows, and corresponding optimized spectral components, said optimized spectral components substantially minimizing said merit function.